Defining parameters
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(128, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 12 | 44 |
Cusp forms | 40 | 12 | 28 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(128, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
128.4.b.a | $2$ | $7.552$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(-64\) | \(q+2\beta q^{3}-3\beta q^{5}-32 q^{7}-37 q^{9}+\cdots\) |
128.4.b.b | $2$ | $7.552$ | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{3}+19q^{9}+5^{2}\beta q^{11}-90q^{17}+\cdots\) |
128.4.b.c | $2$ | $7.552$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{5}+27 q^{9}+23\beta q^{13}+94 q^{17}+\cdots\) |
128.4.b.d | $2$ | $7.552$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(64\) | \(q+2\beta q^{3}+3\beta q^{5}+32 q^{7}-37 q^{9}+\cdots\) |
128.4.b.e | $4$ | $7.552$ | \(\Q(\sqrt{2}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-13q^{9}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(128, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(128, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)